ABSTRACT
During a hypothetical severe accident in a nuclear reactor, a part of the fuel rods may partially melt or even collapse. This leads to a fragmentation of the initially cylindrical fuel rods and formation of a bed of particles (order of magnitude : 1-5 mm ). In order to predict the safety margin of the reactor under such conditions, the coolability of this porous medium and the possibility to reflood the particle bed must be understood. Since particles may reach very high temperatures (possibly above 2000K) when reflooding occurs, the propagation of water through the particle bed occurs under severe flow regimes, in particular film boiling. Flow regimes in particle beds or, more generally, in porous media, cannot be observed easily in experiments. Therefore, they must be postulated from analogies with flow regime maps in pipes or micro-channels. The present paper proposes a model for the non isothermal two-phase flow of water in a porous medium initially at high temperature.
The detailed description of two-phase flow in a debris bed is addressed by a six-equations thermalhydraulic model. The momentum balance equation for each fluid phase is an extension of Darcy’s law. This extension takes into account wall friction but the difficult issue of interfacial drag force between liquid and gas is not addressed in this paper. The energy balance equations of the three phases (liquid, gas and solid phase) are obtained by a volume averaging process of the local conservation equations. The phase change rate is naturally determined without additional phenomenological equation. This model was already derived and assessed in previous papers, in the case of a limited over-heating of the particles (no film boiling). The present paper presents the extension of the model to film boiling regime. The heat exchange coefficients are calculated for the film boiling and transition boiling regimes, for simplified local flow configuration, as a function of the local geometry of the porous medium and the local phase distribution. Analytical determination of effective properties are given in the paper, for simple stratified flows, corresponding to film boiling. The effect of phases velocities on heat transfers is introduced using earlier DNS results.
Calculations of one-dimensional reflooding (from bottom) are compared with experimental data. The results show a fairly good agreement of the produced steam flow rate and the progression of the quench front. The importance of using a nonequilibrium model for temperatures is demonstrated. The comparison with the calculated reflooding of a non homogeneous two-dimensional particle bed is discussed. Particle beds resulting from the collapse of fuel rods are likely to present regions with very different permeabilities. This generates twodimensional flows, with water progressing quickly in the high permeability regions. Simple cases with two regions of differents permeabilities are calculated. It is shown that twodimensional effects may lead to the formation of dry pockets in the center of the bed where quenching is delayed. The effects of injection velocity, particle diameter and pressure are studied.
